Statistical mechanics of ideal particles in null dimension and confinement

The statistical mechanics of ideal particles in null dimension is obtained from a recently given polylogarithm formulation by analytic continuation. The chemical potential behaves anomalously as the dimensionality d→0, where d=0 appears to be an essential singularity of the reduced density. As a result, the temperature becomes irrelevant in null dimension. Also, the exclusion principle reappears in the coordinate space in the guise of an infinitely high energy barrier. Bose particles are not confinable. Standard thermodynamic quantities have been obtained. These results show some relevance to quantum dots in ultrasmall volumes. © 1996 The American Physical Society.